# Video: Finding the Total Surface Area of a Cylinder in a Real-World Context

Determine, to the nearest tenth, the surface area of a tin can with a radius of 8 centimetres and a height of 16 centimetres.

02:26

### Video Transcript

Determine to the nearest tenth the surface area of a tin can with a radius of eight centimetres and a height of 16 centimetres.

This tin can is a cylinder. So we’ll begin with a sketch of the tin can. We’re told that the radius of the tin can is eight centimetres; we’re also told that the height of the can is 16 centimetres. Let’s recall the formula for finding the surface area of a cylinder.

The formula is two 𝜋𝑟 squared plus two 𝜋𝑟ℎ. The first part of this formula two 𝜋𝑟 squared gives the area of the circles on the top and base of the cylinder. The second part two 𝜋𝑟ℎ gives the area of the curved part of the cylinder, which when unfolded forms a rectangle with dimensions ℎ, the height of the cylinder, and two 𝜋𝑟, the circumference of the circles on the top and the base.

Let’s substitute the values of 𝑟 and ℎ for the cylinder in this question. The radius of the cylinder is eight centimetres, so we have two multiplied by 𝜋 multiplied by eight squared for the first term. The height of the cylinder is 16 centimetres, so we have two multiplied by 𝜋 multiplied by eight multiplied by 16 for the second term.

Now, we’ve been asked for our answer to the nearest tenth. So we’ll assume we’re allowed to use a calculator within this question. Evaluating each of the constants gives 128𝜋 plus 256𝜋. Summing these two terms gives 384𝜋.

Now we need our answer to the nearest tenth. So we need to go on and actually evaluate this as a decimal. So using my calculator, we have a value of 1206.371579. Remember the question has asked us for the value to the nearest tenth, so I need to round this answer. I also need to include area units which in this problem are centimetres squared. So we have an answer of 1206.4 centimetres squared for the total surface area of the tin can.